The advantage of a ground "plane" over traces is, it's wider, so the characteristic impedance is lower, giving higher capacitance and lower inductance than traces can (and also making the impedance easier to terminate in bypass capacitors). If you have it neck down a lot, you lose that advantage because now it looks like an electromagnetic dumbbell that resonates at some frequency (probably in the 100MHz range, just guessing from what it looks like). Which can be effectively addressed with bypass caps and stuff, but then you need to be careful of that, too.
It seems like the 5V net doesn't have many connections; I suppose it's also not high speed or low noise? That would be a good candidate to route as a trace (it practically is, already), maybe even on an outer layer (top or bottom).
You want to give priority to nets with lots of connections (routing traces to a hundred pads/vias is a PITA) and low noise nets (analog?), where the lower impedance helps out. You want to avoid noisy circuitry (digital logic, switching supplies?) from overlapping low noise planes. You also want to avoid traces crossing over the gaps between pours -- it's not so bad if ground (opposite inner layer) is contiguous (it acts to bypass the pours, so the coupling from/to the trace is relatively low), or if bypass capacitors are placed beside the traces, nailing down the edges between voltage domains.
Speaking of ground, the ground layer is solid, right?
Tim